Journal of Pharmaceutical Sciences 110 (2021) 2753−2764

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Journal of Pharmaceutical Sciences

journal homepage: www.jpharmsci.org

Pharmaceutics, Drug Delivery and Pharmaceutical Technology

New characterization measures of pore shape and connectivityapplied to coatings used for controlled drug release

Sandra Barmana,*, Cecilia Fagerb, Magnus R€odinga,c, Niklas Lor�enb,c,Christian von Corswantd, Eva Olssonb, David Boline, Holger Rootz�ena

aDepartment of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, 412 96 Gothenburg, Swedenb Department of Physics, Chalmers University of Technology, 412 96 Gothenburg, Swedenc Agriculture and Food, RISE Research Institutes of Sweden, Gothenburg, Swedend Oral Product Development, Pharmaceutical Technology & Development, Operations, AstraZeneca, Gothenburg, Swedene CEMSE Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

A R T I C L E I N F O

Article history:Received 9 November 2020Revised 26 January 2021Accepted 16 February 2021Available online 10 March 2021

* Corresponding author.E-mail address: sandrabarman@gmail.com (S. Barman

https://doi.org/10.1016/j.xphs.2021.02.0240022-3549/© 2021 The Authors. Published by Elsevier In(http://creativecommons.org/licenses/by/4.0/)

A B S T R A C T

Pore geometry characterization-methods are important tools for understanding how pore structure influen-ces properties such as transport through a porous material. Bottlenecks can have a large influence on trans-port and related properties. However, existing methods only catch certain types of bottleneck effects causedby variations in pore size. We here introduce a new measure, geodesic channel strength, which captures adifferent type of bottleneck effect caused by many paths coinciding in the same pore. We further developnew variants of pore size measures and propose a new way of visualizing 3-D characterization results usinglayered images. The new measures together with existing measures were used to characterize and visualizeproperties of 3-D FIB-SEM images of three leached ethyl-cellulose/hydroxypropyl-cellulose films. All filmswere shown to be anisotropic, and the strongest anisotropy was found in the film with lowest porosity. Thisfilm had very tortuous paths and strong geodesic channel-bottlenecks, while the paths through the othertwo films were relatively straight with well-connected pore networks. The geodesic channel strength wasshown to give important new visual and quantitative insights about connectivity, and the new pore sizemeasures provided useful information about anisotropies and inhomogeneities in the pore structures. Themethods have been implemented in the freely available software MIST.© 2021 The Authors. Published by Elsevier Inc. on behalf of American Pharmacists Association. This is an open

access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Keywords:

CoatingControlled deliveryMorphologyPhysical characterizationPolymer(s)

).

c. on behalf of American Pharmacists Association. This is an open access article under the CC BY license

Introduction

The pore geometry to a large extent determines the rate of diffu-sive transport through a porous material. Structural properties thatcan have a large impact on the diffusive transport rates are pore vol-ume fraction; pore sizes and shapes; lengths of paths through thepore system; dead-ends; and bottleneck effects1,2 (because the gov-erning equations are mathematically equivalent, this also holds forelectrical and thermal conductivity3). Information about connectivityproperties such as path lengths and bottleneck effects can only beobtained from 3-D representations of the material. Advances inmicroscopy techniques have made it possible to obtain detailedimages of the 3-D geometry of porous materials.4−6 To make full useof these images, characterization methods that capture the importantproperties of the pore geometry are needed. Nevertheless, despite

the availability of both 3-D images and characterization methods,often only simple measures such as the total porosity,7 the sphericalpore size distribution, or the chord-length distribution8 are reported.In particular, these measures do not give any information aboutanisotropy or about connectivity of pore structures.

Existing pore geometry measures include pore sizes computedusing different structuring elements, such as spheres, ellipsoid, andlines, and local porosity. Path lengths through the pore network arecharacterized by the geodesic tortuosity and measures the length ofgeodesic paths.9 A geodesic path is here the shortest path which liescompletely within the pore space and which connects the top to thebottom and goes through a specified point. Geodesic paths and tortu-osities are powerful methods that can be used to visually explorehow the pore network is connected and geodesic tortuosity is often agood predictor of diffusive transport.10,11 It is well known that bottle-neck effects caused by pore size variation, i.e. constrictivity effects,can have a large effect on transport through porous materials, see e.g.Petersen,1 Van Brakel and Heertjes,12 Dullien13(p. 228) and Siepmann

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et al.2(ch.9) Measures of this type of constrictivity effect have beenintroduced in recent years in Berg14 and Holzer et al.15 In Holzeret al.,15 the constrictivity is computed using pore sizes with respectto structuring elements and from mercury intrusion porosimetry(MIP)-pore sizes that are designed to match a physical experiment.This constrictivity measure together with the tortuosity has beenshown to be a good predictor of diffusive transport.10 Still, existingconstrictivity measures do not capture all aspects of bottleneckeffects.

This paper introduces a new geometric measure, geodesic channelstrength, which quantifies an important property of the network con-necting the pores, viz. parts of the pore structure where many geode-sic paths coincide. The measure provides a method to simplify thenetwork which can be used to visually identify and to quantifyimportant structural features such as bottlenecks in the data and forprediction of diffusive transport. The geodesic channel strengthmeasures a type of bottleneck effect that is different from the alreadyexisting constrictivity measures.

The paper also proposes new measures of the local shape of poresobtained as maxima, taken in different directions, of pore sizes withrespect to circles and lines. These maxima gave additional shapeinformation, which was summarized as elongation and ellipsoid fac-tors. To the best of our knowledge such maxima and shape factorshave not been considered in earlier literature. We further introduce anew way of visualizing results in 3-D by layering images with differ-ent opacities.

Leached ethyl-cellulose (EC)/hydroxypropyl-cellulose (HPC) filmsare used as coating for controlled drug release from pharmaceuticalpellets. The drug diffuses through the pore structure that forms whenthe HPC is leached out, and the pore geometry controls how fast thedrug is released. Previous work detailing the 3-D microstructure ofthis type of EC/HPC polymers can be found in Marucci et al.16,17 andin Andersson et al.,18 where the material has been imaged using con-focal microscopy and scanning electron microscopy. Transportthrough these coatings has been visualized using in situ environmen-tal scanning electron microscopy in Jansson et al.19 The same type ofpolymer has also been characterized with respect to pore shape andbranching points in H€abel et al.,20,21 and a visualization of the inter-connectivity of the three films which are used in this work can befound in Fager et al.22

In the present paper, we used our newmeasures, together with localporosity, pore size with respect to spheres, circles and lines, constrictivitymeasures, and measures based on distances through the pore structure,to extract important features of the pore geometry of 3-D images of EC/HPC films. The images were obtained from combined focused ion beamand scanning electron microscopy (FIB-SEM) tomography of films wherethe aqueous soluble HPC phase had been leached, leaving the EC porousnetwork intact.23 The advantage of using scanning electron microscopyin contrast to, e.g., confocal microscopy is the high spatial resolution, andthe focused ion beam tomography in combination with the scanningelectron microscope enables a 3-D reconstruction of the porous micro-structure. Other sequential imaging techniques that can be used for 3-D

Fig. 1. Cross sectional surfaces, imaged using a FIB-SEM backscatte

reconstruction of porous materials, apart from confocal microscopy24

and electron microscopy,25 are X-ray tomography26 and neutrontomography.27

In the next section the processes used to manufacture the EC/HPCfilms, to leach the HPC phase, to record experimental 3-D data and tobinarize the images are outlined. The following section describes thepore structure characterization methods. The results are then given,followed by a discussion of the main conclusions. Details about theconstruction of the layered images, two videos illustrating the advan-tages with using layered images, and the method used to computethe geodesic paths can be found in the electronic supplementarymaterial.

Materials and methods

Data acquisition

Ethyl Cellulose/Hydroxypropyl Cellulose Polymer FilmsThe polymer films were produced from the water soluble poly-

mer, HPC, and the water insoluble polymer, EC. The two polymerswere dissolved in ethanol and sprayed onto a rotating drum to createa film. The spraying direction was the direction of transport throughthe film, corresponding to the direction of transport through thecoatings of pharmaceutical pellets. After drying, the films were cutoff from the drum and the HPC were leached out to create0.5 cm £ 0.5 cm square porous films. The weight percentages of thewater soluble polymer HPC were 22, 30, and 45. The films weredenoted HPC22, HPC30 and HPC45, respectively. For a detaileddescription of the production process see Fager et al.22

Focused ion beam scanning electron microscopy and 3-D imagesegmentation

A FIB beam was used to sequentially prepare cross sections of theEC/HPC films and a SEM was used to image the cross sections. Thisproduced stacks of 200 2-D images per film. Fig. 1 shows one of the2-D images from each stack. Again, see Fager et al.22 for a detaileddescription. Segmentation of the image data into solid and pore wasperformed in the following fashion: For each data set, manual seg-mentation was performed in 100 randomly selected 2-D regions ofsize 256 £ 256 pixels. So-called linear scale-space features, i.e., a setof Gaussian smoothed images at different scales were extracted(using Gaussian filters with standard deviations sigma = 1, 2, 4, 8, 16,32, 64, and 128 pixels) for the slice to be segmented and five adjacentslices in each direction. These features were used to train a randomforest classifier (combining the output of 101 decision tree classifiers)which is then applied to the full data sets. The resulting segmentedimages (Fig. 2) were used to describe the porous network. For moredetails on the image segmentation, the reader is referred to R€odinget al.,28 in which an almost identical segmentation work flow wasused.

red electron detector, of (a) HPC22, (b) HPC30 and (c) HPC45.

Fig. 2. Binarized pore structures of (a) HPC22, (b) HPC30 and (c) HPC45. Pores are shown in white. The slices were milled away in the z-direction, and y is the direction of diffusivetransport.

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To avoid edge effects the images were cropped close to theboundary, removing 11% of the voxels in the x-direction. The imageswere also sub-sampled, taking every fifth voxel in the x- and y-direc-tion, so that the voxel size was 50 nm in all directions. This was nec-essary since equal voxel size in all directions is a requirement of thebuilt-in Matlab function bwdistgeodesic29 which was used to com-pute geodesic paths, geodesic tortuosity and geodesic channelstrength. The resulting images were of size 500 £ 750 £ 200 voxels.

A slice from each of the three films is shown in Fig. 1 and thebinarized pore structures that the characterization methods wereapplied to are displayed in Fig. 2.

Characterization methods

New Method: Geodesic Channel StrengthThe geodesic channel strength as defined below quantifies how

pores are interconnected. A channel of high strength by this defini-tion is a part of the pore structure where many geodesic paths coin-cide. The channel measure enables the visualization andquantification of main channels, i.e. points with relatively high chan-nel strength. This measure highlights an important property of thenetwork connecting the pores; visualizing only main channels cansimplify an otherwise complex network, making it easier to detectimportant structural features. In some cases when there are channelsof varying strength and some channels have a particularly highstrength it can be concluded that there is a bottleneck effect. How-ever, it is important to also take pore size and alternative pathwaysinto account before drawing this conclusion. A channel of highstrength might not be a bottleneck if it has a large pore size relativeto the pores leading into the channel. Alternative pathways close tothe high strength channel could also reduce the bottleneck effect.

A geodesic path, denoted GeoPath(p), as described in the introduc-tion, is a path that (1) lies completely within the pore space, (2) is theshortest path that connects the top of the pore structure to the bot-tom of the pore structure in the chosen direction (x, y or z),1 and(3) passes through the point p. Computation of shortest paths withrestrictions on the space that can be travelled can be found in robot-ics, visual computing, and image analysis,30,31,32,33 and has been usedin the context of material science in Lindquist et al.34 and in Peyregaand Jeulin9 to visualize paths through a material. The left panel ofFig. 3 illustrates the concept of a geodesic path in a 2-D pore struc-ture. This 2-D network was extracted from a 930 £ 6 £ 750 subset ofthe original binarized HPC45 sample by projection of the six slices inthe y-direction to one slice.

1 Note that the top and bottom of the pore structure refers to the top and bottom inthe chosen direction.

The algorithm used to compute the geodesic channel strength in thethree EC/HPC films was implemented as follows: First, a set S consistingof around 9000 points p were distributed evenly throughout the porestructure. The distribution was done by dividing the pore structure intosmall sections, and randomly placing points p uniformly in each section.The number of points placed in each small section, out of the total 9000points, was proportional to the pore volume of the small section. The cor-responding geodesic path GeoPath(p) (computed in the chosen direction)was then computed for every distributed point p. Each path was set tohave a thickness of 20 voxels (corresponding to 1mm) tomake the chan-nel measure easier to visualize.

This resulted in a set of paths G = {GeoPath(p): p 2 S}. Finally, thegeodesic channel strength, denoted GeoChannel(p'), is defined as thepercentage of paths in G that passed through the point p'. GeoChannel(p') was computed for all points p' in the pore structure. See the elec-tronic supplementary material for a description of the algorithm forcomputing the geodesic paths.

An example of the geodesic channel measure is shown in the rightpanel of Fig. 3. It clearly shows a significant aspect of the 2-D networkconnecting the top and bottom: there are four main channels from themiddle to the top, whereas there are only three main channels from themiddle to the bottom. Note also that the three geodesic paths GeoPath(p)in the left panel follow to a large extent the main geodesic channels,except when the paths are close to their respective points p.

Geodesic tortuosityThe point-wise geodesic tortuosity is defined as

tdir pð Þ ¼ l GeoPath pð Þð Þ=L;where l(GeoPath(p)) is the length of the geodesic path corre-sponding to p, computed in direction dir, and L is the thicknessof the pore structure in this direction. The tortuosity thus meas-ures the length of the geodesic path relative to the length of thepore structure in the direction the path is computed. A 2-D exam-ple of the tortuosity is shown in Fig. 4, where the color of eachpoint corresponds to the point-wise tortuosity-value in thatpoint. It is clear from the tortuosity that geodesic paths on theleft are longer than paths on the right (compare with the threepaths shown in Fig. 3).

Our definition computes the tortuosities for the full pore struc-ture, as is done in Peyrega and Jeulin9 and Barman et al.,11 instead ofusing the common method where tortuosities are only computed forgeodesic paths at the top layer of the pore structure (i.e., tortuositiesare only computed corresponding to geodesic paths GeoPath(p) forpoints p in the top layer).10,34 In Barman et al.,11 computing tortuosi-ties for the full pore structure was found to give better diffusivetransport prediction.

Fig. 3. Example illustrating the connection between geodesic paths and geodesic channel strength on a 2-D pore structure extracted from HPC45. Left: Three geodesic paths GeoPath(p). The points p, for which GeoPath(p) is the shortest path connecting p to the top and the bottom, are marked with yellow circles. The matrix is shown in black. Right: The geodesicchannel strength computed from 3000 geodesic paths connecting the top and bottom. The channel strength is only shown for pores that are connected to the top and bottom. Thematrix and pores that are not connected are shown in black. Double-headed arrows indicate the direction of the geodesic paths and channel strength. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version of this article.)

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Local porosityThe local porosity was computed similarly to what was done in

Hilfer,35 by computing the porosity for subsets of the pore structure:The pore structure was first divided into 45 £ 30 £ 3 boxes, i.e. the x-direction was divided into 45 parts of roughly equal size, the y-direc-tion into 30 parts of roughly equal size, and the z-direction into3 parts of roughly equal size. The porosity was then computed for

Fig. 4. Examples, using the same pore structure as in Fig. 3, showing circle-pore sizes, maximresponding to paths connecting the top and bottom. Arrows indicate the direction the conneare connected to the top, and tortuosity values were only computed for pores that are conne

each combination of 3 £ 3 £ 3 neighboring boxes, resulting in localporosity values on a 43 £ 28 £ 1 grid.

Local pore sizesLocal pore sizes are computed relative to simple geometrical

objects, which are called structuring elements. The pore size in apoint p is defined as the size of the largest rescaled structuring

al line-pore sizes, MIP-pore sizes computed from the top and geodesic tortuosities cor-ctivity measures were computed in. MIP-pore sizes were only computed for pores thatcted to the top and bottom.

Table 1Pore shape measures and the two pore shape factors. The mean, minimum, maximum and standard deviation of the sphere-pore size pssphere, maximal circle-pore size pscirc,max, andmaximal line-pore size psline,max are given inmm.

HPC22 HPC30 HPC45

pssphere, mean (min, max) [st.dev.] 0.35 (0.05, 0.95) [0.14] 0.60 (0.05, 1.55) [0.26] 0.72 (0.05, 2.15) [0.36]pscirc,max, mean (min, max) [st.dev.] 0.62 (0.05, 2.95) [0.35] 1.00 (0.05, 2.55) [0.39] 1.18 (0.05, 3.15) [0.52]ellipsoid factor 2.0 1.9 2.0psline,max, mean (min, max) [st.dev.] 1.42 (0.05, 11.95) [0.99] 2.57 (0.05, 8.55) [0.94] 3.39 (0.05, 11.75) [1.32]elongation factor 4.7 5.3 6.3

2 https://mist.math.chalmers.se

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element that can fit within the pore space and cover p. Each point inthe pore space is in this way given a local size. These local pore sizesprovide an intuitive measure of size for pore geometries for whichthere are no well-defined pore shapes. Local pore sizes, or granulo-metries as they are also called, were introduced in Matheron36 and isa common tool in image analysis.33 Different structuring elementsquantify different properties of the pore geometry. For the 3-D datawe used spheres, circles and line segments as structuring elements.The sphere-sizes give non-directional size information, whereascircles and line-sizes give information about pore shape and anisot-ropy. The notation for the structuring elements is Bsphere for a spherestructuring element, Bcirc,plane for a circle located in the plane, wherethe plane is either of the sub-planes (x, y), (x, z), or (y, z), and Bline,dirfor a line segment structuring element in direction dir, with dir beingthe direction of the x-, y-, or z-axis, a diagonal direction in the (x, y)-,(x, z)- and (y, z)-planes, or a diagonal direction in the unit cube. Thusthree circle-sizes and 13 line-sizes are computed. The local pore sizeis denoted ps* for structuring element B*.

We also define two new local pore size measures: the local maxi-mal circle-pore size pscirc,max, which is obtained by taking the maxi-mum of pscirc,plane over all three planes, and the local maximal line-pore size psline,max, which is obtained by taking the maximum ofpsline,dir over all thirteen directions. These maximal pore sizes areused to define an elongation factor and an ellipsoid factor that sum-marize the shape of the pores. The factors are defined by comparingthe maximal circle size and the maximal line size respectively to thesphere size, and taking the mean over all points in the pore space, asElong = mean(psline,max/pssphere) and Ellips = mean(pscirc,max/pssphere).2-D illustrations of circle-pore sizes and maximal line sizes are shownin the top of Fig. 4.

MIP-pore sizesThe MIP-pore size in a point p, denoted psMIP,dir, is the size of the

largest sphere that can travel through the pore space from the top ofthe pore structure in the chosen direction to the point p, and that cancover p. The MIP-pore size measure is illustrated in Fig. 4.

The ratio between the median MIP-bottleneck size, median(psMIP),and the median of the sphere-pore size, median(pssphere), is termedthe constrictivity. The MIP-pore size and the constrictivity has previ-ously been proven useful as measures of interconnectivity and bottle-neck effects.10,37,38

Computation

The spheres, circles, and diagonal line-segment structuring ele-ments that were used to compute the local pore sizes are approxima-tions of the ideal shape on the finite grid of the microscopy image.33

This approximation is better for larger structuring elements. Forcomputational efficiency, not all possible local pore sizes were com-puted. For the algorithm to compute the local MIP-bottleneck size,see M€unch and Holzer.39

The characterization methods were implemented in Matlab.29 Thegeodesic tortuosity, geodesic paths and geodesic channel strengths werecomputed from the geodesic distance transform obtained from the

Matlab function bwdistgeodesic. The algorithm that was implementedfor computing the geodesic paths is given in the electronic supplemen-tary information. The geodesic tortuosity was obtained directly from thegeodesic distance transform, and the geodesic channel strength wascomputed from a collection of geodesic paths as described above. The3-D visualizations of characterization results were created using Para-view.40 The image layering (see the electronic supplementary material)can be done in most image editing software, here it was done usingInkscape.41 The videos in the electronic supplementary material werecreated using Paraview and VideoPad Professional.42

All characterization methods have been implemented in the freelyavailable software MIST,43 which soon will be available to downloadfrom here.2

Results

The porosity for the three EC/HPC films was calculated to 18% forHPC22, 29% for HPC30 and 42% for HPC45. The measured pore vol-ume fractions in the cropped images that were used for the charac-terization, which had voxels close to the x-direction removedbecause of edge effects from the binarization, were relatively close tothose of the original binarized images, with 18% for HPC22, 30% forHPC30 and 41% for HPC45.

The characterization results are inevitably biased because of bound-ary effects. The sample size is much smaller in the z-direction, whichshould result in stronger boundary effects in the z-direction. However,since the sample sizes in the x- and y-direction are similar, the results forthese directions are comparable and hence some of the results are givenonly for the x- and y-directions. Additionally, the most interesting resultsare for the y-direction, the direction corresponding to drug transport,and some results are only presented for this direction.

Pore size and shape

Table 1 shows that the sphere-pore sizes, maximal circle-poresizes and maximal line-pore sizes increase as the pore volumeincreases (with the exception of the max value of the maximal circle-and of the maximal line-pore size, which is high for HPC22 due toinhomogeneities, see the discussion below). The sphere-sizes are alsosmaller than the circle-sizes which in turn are smaller than the line-sizes, as can be expected. The same trends are observed in Fig. 5. Theellipsoid shape factor stays relatively constant, whereas the elonga-tion shape factor increases as the pore volume increases (Table 1).

What stands out in Fig. 6 is that there is a big difference in how oftenthe line size in the x-direction (numbered 1) is the largest compared tohow often the line size in the y-direction (numbered 2) is largest. Thisline size trend is relatively strong in all films, but is stronger for lowerpore volume fractions. The same trend with smaller sizes in the y-direc-tion can be found for the diagonal lines in the planes (numbered 4-9) forHPC22, i.e., the diagonal lines are more frequently the largest in thexz-plane (numbered 8-9) compared to lines in the planes that include

Fig. 5. Densities of sphere sizes, maximal circle sizes and maximal line sizes, for all three films.

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the y-direction (numbered 4-7). The four cross-diagonal lines in the unit-cube (numbered 10-13) do not show large differences between the dif-ferent directions.

The HPC22 film is seen in Panel (b) of Fig. 7 to have strongly inhomo-geneous xz-circle sizes, i.e. pscirc,xz varies markedly between y-slices. Thisis, however, not the case for HPC30 and HPC45 in Panel (b), nor is it thecase for the other two circle-pore sizes, pscirc,yz and pscirc,xy for any of thethree films (Panels (a) and (c)). The largest value of the maximal circle-pore size pscirc,max (and of the maximal line-pore size psline,max) is alsolarger for HPC22 than for HPC30 (Table 1), which goes against the trendof pore sizes increasing with increasing porosity.

Connectivity

By Table 2 the proportion of connected pores is much lower inHPC22 than in HPC30 and HPC45. The MIP-pore size and the constric-tivity show that bottleneck effects caused by variation in pore size arestronger in HPC22 than in the other two films. The median MIP-poresize of HPC22 corresponds to bottlenecks of one voxel, meaning thatthe largest sphere that can reach at least half of the film from the topis a sphere that consists of only one voxel.

Fig. 6. The frequency of points in the pore space for which the line size in the chosen directdirections are numbered, showing the frequency for (1) the x-direction, (2) the y-directionplane and (8-9) the xz-plane, and (10-13) the four diagonal directions crossing the unit cubecolours (red, yellow/green, blue) are the same as in the numbering of the histogram-bars. (Fothe web version of this article.)

The local porosities shown in Fig. 8 are averages of the porosity inboxes that span the whole film in the z-direction but that only occupya small portion of the film in the x- and y-direction. The figure showsthat there is quite high variation in all three films, and that there arelayers in the y-direction with low porosity (see the layers markedwith a dashed frame in the figure).

Visual inspection of geodesic pathsThe geodesic paths computed in HPC22, shown in Fig. 9, seem

more disordered than the paths through HPC30 and HPC45, whichare more evenly distributed throughout the pore space and whichare less winded. The layers in HPC22 with low porosities (markedwith a dashed frame in yellow in Fig. 8) are marked with a yellowbox. It looks as though the connectivity, through this layer is poor, asthe computed geodesic paths all pass through two parts of this box,see the yellow arrows.

Connectivity measured by geodesic tortuosity (path lengths)For the tortuosity (Table 2 and Figs. 10 and 11), the lengths of

paths in HPC22 are considerably larger than the values in the othertwo films, for both tx and ty. For ty in HPC22, which is the tortuosity

ion is larger than the line size in all other directions, shown for all three films. The lineand (3) the z-direction, the two diagonal directions in (4-5) the xy-plane, (6-7) the yz-. The line directions are illustrated in the box in the lower left corner, and the three liner interpretation of the references to color in this figure legend, the reader is referred to

Fig. 7. The mean of (left) pscirc,yz, (middle) pscirc,xz and (right) pscirc,xy, computed for each slice in the direction perpendicular to the respective circle, i.e., the mean of the circle-poresize over each slice in (left) the x-direction, (middle) the y-direction and (right) the z-direction. Each curve was normalized by dividing by the mean of the respective circle-poresize computed over the full pore space. The circle orientations are illustrated in the boxes below the figures.

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in the transport direction, the left half of the film is poorly connectedwith ty values above three (light blue areas). There is an area in theright half of the film which is better connected with ty around two(dark blue areas). The area with dark blue tortuosity in the yellowbox corresponds to the part indicated by the yellow arrow on theright of HPC22 in Fig. 9.

The values of the tortuosities of tx in HPC22, and of both tx and tyin the other two films, are more homogeneously distributed through-out the films. The relative lengths of paths in the transport direction(ty) are about twice as large as the relative lengths of paths in the x-direction (tx) for HPC22. Paths in the transport direction are longerthan paths in the x-direction for HPC30 as well, but the difference issmaller. For HPC45, the difference is quite small, except for the max-values. The pores in the layers with low porosities in Fig. 8 (markedwith dashed frames), can be seen in Fig. 10 to have relatively hightortuosities in the x-direction. This trend is strongest in HPC22.

Connectivity measured by geodesic channel strength (path locations)The main channels, i.e. parts of the pore structure with high geo-

desic channel strength, are of considerably higher strength in HPC22compared to in HPC30. The yellow box in HPC22 in Fig. 12 contains amain channel with strength of 86%, i.e. 86% of all computed geodesicpaths or around 8000 of the total 9000 computed geodesic paths,

Table 2Pore connectivity measures for the three films computed in the y-direction, showing the prostrictivity, the tortuosity (also computed in the x-direction) and the channel strength. The msize, the tortuosity, and the channel strength. The MIP-pore size values are given inmm.

HPC22

Proportion connected pores, y-dir. 0.86psMIP,y, median (min, max) [st. dev.] 0.05 (0.05, 0.75) [0.07]Constrictivity, y-dir. 0.15tx,, median (min, max) [st. dev.] 1.27 (1.11, 2.17) [0.13]ty,, median (min, max) [st. dev.] 2.75 (2.07, 4.62) [0.49]GeoChannelsy, median (min, max) [st. dev.] 0.012 (0.0001, 0.86) [0.060]

passed through this channel. In fact there are only two paths whichconnect the pore space above the yellow box with the pore spacebelow; one on the left (main channel in gray with channel strength14%) and the one mentioned above on the right (main channel in redwith channel strength 86%). If these main channels were closed, thepore structure would no longer be connected, indicating that thearea marked by the yellow box is a limiting layer that has a consider-able effect on the connectivity of HPC22. The lowest tortuosities com-puted in the y-direction for HPC22 (Fig. 10, top left, dark blue pores),with values around two, correspond to geodesic paths that passthrough the main channel on the right.

In contrast, the maximum geodesic channel strength in HPC30and HPC45 are both under 11%, meaning that the paths are morewell distributed across the whole pore space (Table 2) These differen-ces in channel strengths between the films are also clearly visible inthe histograms in Fig. 13.

Discussion

Pore shape: Since the ellipsoid-factor throughout was roughlyequal to 2, the pores are relatively flat, and not spherical. The increas-ing elongation factors show that the shape of the pores neverthelesschange with increasing porosity.

portion of pores that are connected to the bottom and top, the MIP-pore size, the con-edian/mean, minimum, maximum and standard deviations are given for the MIP-pore

HPC30 HPC45

0.99 0.990.35 (0.05, 1.15) [0.08] 0.50 (0.05, 2.35) [0.18]0.58 0.671.10 (1.06, 1.43) [0.02] 1.08 (1.04, 1.38) [0.02]1.19 (1.10, 1.55) [0.04] 1.10 (1.04, 1.55) [0.02]0.005 (0.0001, 0.11) [0.012] 0.004 (0.0001, 0.06) [0.006]

Fig. 8. Local porosity, computed for overlapping boxes resulting in values on a 43 £ 28 £ 1 grid. The dashed black frames indicate layers in the y-direction with low local porosity.The dashed frame is filled in with yellow with low opacity in HPC22, corresponding to the yellow boxes used for HPC22 in Figs. 9, 10 and 12. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)

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Inhomogeneity: The films were manufactured by depositing layers,one after the other, in the xz-plane. This may explain why the linesize typically is shorter in the y-direction than in the x-direction, andwhy the variation in circle pore sizes pscirc,xz across slices is large inthe y-direction for HPC22, but not in the other two circle pore size-directions. The sequential deposition of layers could also explain thehigh variation in local porosity in the y-direction in all three films, aswell as the large difference found in connectivity, as measured by thetortuosity, in the x-direction compared to in the y-direction for bothHPC22 and HPC30. This is interesting since the y-direction would bethe direction of transport of drug through the films.

Percolation threshold: 22% pore volume fraction is close to the per-colation onset for this material.16 This means that above porosity 22%there is a sharp increase in how much HPC that is leached out, andthus a sharp increase in how large proportion of the HPC that is con-nected to the top and bottom of the unprocessed film. This mayexplain why the connectivity was much lower for HPC22 than for

Fig. 9. 200 randomly chosen geodesic paths GeoPath(p) for HPC22 (left), HPC30 (middle) anrow). The point p is shown for each path as a black sphere and the directions the paths wereHPC22 is marked with a yellow box. The only two pathways through the yellow box taken byto color in this figure legend, the reader is referred to the web version of this article.)

HPC30 and HPC45, as measured by the proportion of connectedpores, the constrictivity, the geodesic tortuosity and the geodesicchannels (Table 2 and Figs. 8-13). It may also explain why there ismuch larger variation in the circle pore size pscirc,xz across slices inthe y-direction for HPC22 compared to in the other two films. SeeFager et al.44 for a detailed analysis of the diffusive transport proper-ties of the three films, where it was concluded that the low connec-tivity in HPC22 considerably lowers the transport rate through thefilm.

Bias factors: The characterization results were influenced byboundary effects, effects of the binarization algorithm and effectsof the sub-sampling done to obtain equal voxel distance in alldimensions. The influence of these bias factors are difficult toestimate. But since all three films have been treated in the sameway, the characterization results should nevertheless be compara-ble between the three films. Even so, the different properties ofthe films may cause the bias to be different in different films. The

d HPC45 (right), computed in the y-direction (top row) and in the x-direction (bottomcomputed in are indicated by double-headed arrows. A layer with poor connectivity inthe geodesic paths are indicated by yellow arrows. (For interpretation of the references

Fig. 10. Tortuosity for HPC22 (left), HPC30 (middle) and HPC45 (right), computed in the y-direction (top row) and in the x-direction (bottom row). The directions are indicated bydouble-headed arrows. A layer with poor connectivity in HPC22 is marked with a yellow box, and a yellow arrow corresponding to the yellow arrows on the right side of HPC22 inFig. 9 is shown in the top left panel. The color scales: The same opaque color scale has been used for all six combinations of film/tortuosity direction. The difference in color lightnessalong the color scales is due to a layering of images of the tortuosity thresholded at the 10%, 25%, 50% and 100% quantile, with each image layer having a different opacity. See thesupplementary material for more information about the image layering-method. The 10%, 25%, 50% and 100% quantiles are marked with vertical lines on the color bars. The colorbar is shown cut off just above 1.5 for HPC30 and HPC45. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

S. Barman et al. / Journal of Pharmaceutical Sciences 110 (2021) 2753−2764 2761

proportion of connected pores should equal one if the whole filmhad been imaged, since the pores are leached out and thereforepores that are visible in the FIB-SEM images are pores that areconnected to the boundaries of the film. That the proportion con-nected pores in HPC22 is much lower than in the other two filmscould be a combination of the bias factors and the low connectiv-ity of the pores in HPC22. Similar effects could cause the tortuos-ity and channel results to be more biased for HPC22 as comparedto the other two films.

Fig. 11. Histograms of the

New connectivity measure: The geodesic channel measure wasfound to provide interesting information about the pore struc-tures, and in particular showed a big difference between HPC22and the other two films. Even though both the tortuosity andchannel measure are computed based on geodesic paths, the twocharacterization measures highlight different properties of thepore geometry (compare the top row of Fig. 10 with Fig. 12). Themain geodesic channels for example show that paths throughHPC22 are not just longer compared to the paths in the other

data shown in Fig. 10.

Fig. 12. Geodesic channel strength, computed in the y-direction (indicated by the double-headed arrows) from 9000 geodesic paths, shown for all three films. A layer with poorconnectivity in HPC22 is marked with a yellow box and two main channels through the box are indicated by yellow arrows. The color scales: The same opaque color scale has beenused for all three films. The difference in color lightness along the color scales is due to a layering of images of the channel strength thresholded at the 97%, 99.5% and 100% quantile,with each image layer having a different opacity. See the supplementary material for more information about the image layering-method. The 97%, 99.5% and 100% quantiles aremarked with vertical lines on the color bars. The geodesic path illustrations from Fig. 9 are shown to the left of the corresponding geodesic channel strength. (For interpretation ofthe references to color in this figure legend, the reader is referred to the web version of this article.)

2762 S. Barman et al. / Journal of Pharmaceutical Sciences 110 (2021) 2753−2764

two films, as shown by the tortuosity, but behave in a radicallydifferent way. This is especially noticeable in the limiting layer(marked with a yellow box in Figs. 9, 10 and 12), through whichthere are two main channels that all 9000 computed geodesicpaths pass through (indicated by yellow arrows in Fig. 12). Asthese are the only two pathways through the limiting layer, andthe pore size is relatively small, we can conclude that there is astrong geodesic channel-bottleneck effect caused by the pore net-work structure in HPC22. This type of bottleneck is not capturedby the existing constriction-bottleneck measures found in Berg,14

Holzer et al.15; and Stenzel et al.10

Fig. 13. Histograms of the

New pore size measure: Taking maxima of pore sizes with respectto elongation and lines, and computing ellipsoid and elongation fac-tors extracted interesting information about anisotropy in the threeEC/HPC films.

Conclusions

In contrast to the common reporting of only porosity7 and isotro-pic pore size measures, we have shown how the wider range of poregeometry characterization methods applied in this work can be usedto identify interesting properties of the pore geometry of the EC/HPC

data shown in Fig. 12.

S. Barman et al. / Journal of Pharmaceutical Sciences 110 (2021) 2753−2764 2763

films. Anisotropy results, showing a different behavior in the y-direc-tion, i.e. in the direction of mass transport, which could be explainedby the film-manufacturing process, were found. The HPC22 film wasfound to have considerably lower connectivity (Figs. 9-13, Table 2),to be less homogeneous and to have stronger anisotropy (Figs. 6-8,10-13; Tables 1 and 2) compared to the other two films. This could beexplained by the fact that HPC22 is close to the percolation threshold.The new geodesic channel measure also provided insights into theconnectivity, complementing existing connectivity measures such asthe geodesic tortuosity and constrictivity. The bottleneck effectscaused by the pore network in HPC22, measured by the geodesicchannel-strength, considerably lowers the diffusive transport rate inthat film compared to in HPC30 and HPC45, see Fager et al.44

Author contributions

All authors participated in defining over-arching research goals,analysis of results and editing of the manuscript. S. Barman, advisedby D. Bolin and H. Rootz�en, invented and implemented the new char-acterization methods and drafted the manuscript. C. Fager, advisedby E. Olsson, performed the microscopy imaging of the EC/HPC filmsand participated in drafting the manuscript. M. R€oding performedthe segmentation of the image data.

Supporting information available

Supporting information is available electronically. The .pdf-filecontains information about the method used to compute the geodesicpaths, as well as more detailed information about the method thatwas used to create the layered images. A comparison is madebetween layered images and the result obtained with standard 3-Dvolume renderings. There are also two videos which illustrate theconnection between the layered images and successive thresholdingof the 3-D results.

Conflicts of interest

There are no conflicts to declare.

Acknowledgments

We thank Aila S€arkk€a and everyone involved in the SSF project forvaluable feedback. We also appreciate the feedback given at work-shops organized by the Chalmers center SuMo Biomaterials andwithin the project COSIMA, both funded by Vinnova. Funding: Thiswork was supported by the Swedish Foundation for StrategicResearch [grant number AM13-0066], the Knut and Alice Wallenbergfoundation [grant number 20012.0067], and the Swedish ResearchCouncil [grant number 2016-04187].

Supplementary materials

Supplementary material associated with this article can be foundin the online version at doi:10.1016/j.xphs.2021.02.024.

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